A good infantryman could get three shots off a minute as Chewie mentions above. And in terms of the effects of battle, many soldiers with all the shots and orders and explosions going off all about them tended to misfire or not pull the trigger at all, and then continue to load again. After the battle of Gettysburg, they collected all the weapons off the battleground so that they could possibly be reused. Of the 27,000 rifles they collected, 24,000 of them were still loaded. and one made the record at 23 minie balls, 63 buckshot, and quite a bit of powder in it.
Now, in terms of the melee system, there is little chance they would not include it, considering that this war was for the most part fought with the tactics of the Napoleonic Wars, which was in essence to fire a volley or two into the enemies ranks, followed by a rousing call and thrust of steel into the 'blagards.' The men were also taught the use of close-ranged fighting, against saber and against other bayonets while in training. Here I would suggest the perusal of McClellan's Manual of Bayonet Exercises (<---- linked in the name) that he translated from various French drill books and adapted to the US system. This manual pertains to both sides, as both were taught the same thing, if not from the same book on occasion.
And, again as Chewie mentioned above, very few people went back to the hospital following a dance with the business end of a bayonet. Fewer than 5,000 cases from the whole war, at least from Union medical records, were of soldiers with bayonet wounds.
Plus, I am not sure how many of you are familiar with the shape of the bayonets used by Springfield and Enfield Rifled-Muskets, but their shape is banned by the Geneva convention, though for good reason. The triangular shape of the bayonet makes it incredibly difficult for a surgeon to patch the wound up. And, even if he did, as soon as the patient moved the wound would open right back up and become infected.
I am thinking I will make a separate thread to post information about the medical field of the Civil War, considering that is a lecture and a half in itself...